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Abstract

A method is presented for sensing atmospheric wave-front tilt from
a laser guide star (LGS) by observing a laser beacon with auxiliary
telescopes. The analysis is performed with a LGS scatter model and
Zernike polynomial expansion of wave-front distortions. It is shown
that integration of the LGS image over its angular extent and the
position of the auxiliary telescope in an array reduce the tilt sensing
error associated with the contribution from the downward path. This
allows us to single out only the wave-front tilt of the transmitted
beam on the uplink path that corresponds to the tilt for the scientific
object. The tilt angular correlation is analyzed in the atmosphere
with a finite turbulence outer scale. The tilt correlation angle
depends on the angular size of the telescope and the outer scale of
turbulence. The tilt sensing error increases with the auxiliary
telescope diameter, suggesting that an auxiliary telescope must be
small. The Strehl ratio associated with the contribution from the
downward path is in the range from 0.1 to 0.9 when the relative
telescope diameter D/
r0 varies from 4 to 93
and the turbulence outer scale is in the 10–150-m range. Tilt
correction increases the Strehl ratio compared with the uncorrected
image for all the system parameters and seeing conditions
considered. The method discussed gives a higher performance than
the conventional technique, which uses an off-axis natural guide
star. A scheme for measuring tilt with a beam projected from a
small aperture is described. This scheme allows us to avoid
phosphorescence of the main optical train for a sodium LGS.

References

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